In the Name of Allah,
Praise be to Allah,
Some people may, when the teacher makes a mistake, yell out "You're wrong!" or something like "That's incorrect!". However, this is not proper. If one sees that the teacher has made a mistake, he should say it politely and gently.
This is from the good manners of a Muslim, because if he were to yell out a teacher's mistakes, this could greatly influence the teacher's feelings, so the Muslim should instead say it in a good manner. Correcting mistakes is something important because if one's mistakes were never corrected, he would remain upon ignorance. Correcting mistakes is also beneficial, the teacher would learn of his mistake and gain the proper knowledge of what he was trying to teach.
It is also a must that if the teacher doesn't know something, he should say "Allāh knows best.". Because of this, Allāh will reward him with the knowledge that he didn't previously know before through either the teacher's own research or his own students. Allāhu akbar.
May Allah bless you, and shukran.
© Nasir ibn Saleem